When women did speak, men drew on a thesaurus of contempt to describe their voices. In 17th-century America, women characterised as a "scold", "nag" or just plain "unquiet" were submerged on a ducking-stool. As late as the 18th and 19th centuries it was argued that if women persisted in speaking in public, their uteruses would dry up. Henry James compared the female voice to the "moo of the cow, the bray of the ass and the bark of the dog".

One might imagine that the invention of the megaphone, loudspeaker and microphone would have challenged the belief that women made poor orators because their voices weren't sufficiently powerful. And yet this is where we find some of the most blatant prejudice. According to Bell Laboratories in 1927: "The speech characteristics of women, when changed to electrical impulses, do not blend with the electrical characteristics of our present-day radio equipment." The fault lying obviously with the women rather than the equipment.

This characterisation of women's voices as somehow deficient is an enduring theme in the history of broadcasting, dogging women's attempts to get on air. According to the Daily Express in 1928: "Some listeners-in go so far as to say that a woman's voice becomes monotonous after a time, that her high notes are sharp, and resemble the filing of steel, while her low notes often sound like groans."

Women were indicted for conveying too much personality through their voices (the Sunday Dispatch in 1945: "Critics consider that women have never been able to achieve the 'impersonal' touch. When there was triumph or disaster to report, they were apt to reflect it in the tone of their voices") and too little ("For some reason a man … can express personality better by voice alone than can a woman" – Southern Daily Echo in 1928) – or sometimes both at the same time. It was a catch-22, argues Jean Seaton, the official historian of the BBC: either women were deemed too emotional for broadcasting or, if they weren't, then they weren't proper women.

Certainly women were not mute in the early days of the BBC. The first female comedian Helena Millais, "Our Lizzie", made her debut in November 1922. In 1944, Audrey Russell became the first and only British woman to be accredited as a war correspondent. Others who played a prominent cultural role – such as Virginia Woolf, or the composer Ethel Smyth – broadcast regularly. But, as Seaton remarks, women weren't permitted to take on positions such as announcers and newsreaders in which the audible authority of the BBC was invested.

On 21 August 1933, Mrs Giles Borrett stormed the ramparts, reading the BBC six o'clock evening news bulletin for the first time (going under her husband's name, as was customary at the time). BBC officials declared the experiment a failure because female listeners didn't like listening to a woman – the culprit once again presumed to be her own sex.

As with so many of the professions, the war was a breakthrough for women, enabling them to fill posts in radio vacated by men who'd been called up, their timbre reminding male listeners of home. But although it's no longer surprising to hear female voices, from Annie Nightingale to Jane Garvey, on air, the old rationale for their marginalisation proved remarkably resilient. As recently as 1999, the head of news and speech of a commercial radio station in Manchester described a potential recruit to Janet Haworth, a lecturer in broadcasting, as "a great reporter, a very good journalist, but I couldn't put her on air with that voice. She sounds like a fishwife or a washerwoman" (in Women and Radio, edited by Caroline Mitchell). The "acceptable" female radio voice of today – that of, say, Charlotte Green and Harriet Cass – occupies such a narrow pitch range that it's protected from any such charge. That only one in five of the Today programme's guests and reporters are female is eloquent testimony not only to editors' belief that female experts aren't available (thewomensroom.org.uk found 40 in 48 hours last November after Today failed to find one) but also that a woman needs to be exceptionally prominent to earn the right to speak. And young: a report by Skillset for Sound Women, a support group set up in 2011 for women working in audio, found that only 9% of women working in radio are aged 50 and over, compared with over 19% of men.

If, as Simone de Beauvoir argued, women are made, not born, then the voice is one of the ways in which we are made male or female, through which we perform our gender. And this changes over time. Seaton notes that the (corseted) educated women who broadcast in the 30s and 40s in the Received Pronunciation now so out of favour had high, thin, strangulated, crystalline voices, like the Queen (who herself no longer sounds quite so much like the Queen). Joan Bakewell struggled to erase the Lancashire from her voice after hearing her fellow students at Girton, possessing voices that sounded like they could boom across the entrance hall of Harrods; now, on occasion, she's told she's too posh to broadcast. When Radio 5 Live was launched in 1994, an editor asked Bridget Kendall, the BBC's diplomatic correspondent, "Do you think when you go on 5 Live you could lower your voice a social class or two?" She declined.

Bakewell and Seaton think the broadcast voice has become more relaxed and colloquial, something Bakewell attributes partly to the influence of immigrant voices in Britain. And yet women still aren't broadcasting on their own terms: the favoured female broadcast voice today is deep, dark and decidedly un-girly – molasses rather than icing sugar. To be taken seriously, and exhibit gravitas and authority, women need to sound as far as possible like men, even if this isn't their natural timbre, as Margaret Thatcher's disconcertingly deepening voice demonstrated. The female voice, unlike the male, still needs to be pleasing – musical, with varied pitch and clear diction, according to the speech therapist Christina Shewell. Would a woman with the BBC business editor Robert Peston's amusingly idiosyncratic intonation – all elongated vowels and curious consonant stresses (there's a Facebook "Help raise funds to send Robert Peston for speech lessons" page) – have ever got on air?

John Berger wrote in Ways of Seeing that "men act and women appear. Men look at women. Women watch themselves being looked at." To which you could add that, until recently and often still today, men listen to women and women hear themselves being listened to, by a man, to whom the disembodied female voice was always disturbing. The German philosopher Theodor Adorno argued that "Male voices can be reproduced better than female voices. The female voice easily sounds shrill … in order to become unfettered, the female voice requires the physical appearance of the body that carries it." When, in the 1980s, American National Public Radio had three prominent female broadcasters, resentful male colleagues dubbed them the Fallopian Troika. Interestingly, when BBC TV started in 1936, the first presenters ("hostess-announcers") broadcasting from Alexandra Palace were two women, Jasmine Bligh and Elizabeth Cowell. Surely this was because television itself could re-embody women?

Evolutionary psychologists have argued that the link between the female voice and sexuality is genetic and physiological, as men and women rate women's voices as more attractive when they're recorded during the peak fertility period of a woman's cycle. But what's construed as an attractive sound is historically and culturally shaped, as is the fact that men's voices are heard as disembodied, but women's as pure body: women are sound and men language, even though, as Kaja Silverman pointed out in The Acoustic Mirror, generally it's women – either as mothers, nursery workers or teachers – who induct the infant into speech.

The source of this continuing anxiety around the female voice lies in utero: it's the first voice we hear, and feel. Forever associated with matters internal, subjective and corporeal, the mother's voice, as Silverman argues, must be repudiated. The idealisation of the maternal voice and the denigration of the supposedly erotic voice – two sides of the same coin.

No wonder the speaking woman needs to be made an example of. Echo, the talkative nymph punished by Juno with the loss of her voice, is left able only to repeat other's words. King Tereus rapes Philomela and then, to silence her, cuts out her tongue. Hans Christian Andersen's (and later Disney's) Little Mermaid trades in her voice for a human life with legs.

Some of the most thrilling women's voices have emanated from outside broadcasting, in music and performance: Laurie Anderson turned her voice into a machine. Riot grrrl bands emerged out of punk in the 1990s, their very name an extended growl. Susan Philipsz won the 2010 Turner prize for exploring, in a melancholy voice, the relationship between the voice, the body and place. Maggie Nicols, jazz singer and improviser extraordinaire, demonstrates the formidable array of sounds of which the human voice is capable: In "Her noise", an international symposium on the female voice in Oslo last month organised around the her noise archive of women and sound, a hall of men and women sobbed through her keening and howling, rasping and quivering. Voices such as these are not demure or afraid – of being sexual, or unaesthetic, of being emotional and sounding authoritative at the same time, of being too loud, or too high, or too frothy.

• Anne Karpf presents "Archive on 4: Spoken Like a Woman" on BBC Radio 4 on 2 February at 8pm. She is the author of The Human Voice (Bloomsbury).

• This article was amended on 4 February 2013 to restore a preposition cut in the editing process. The original described Janet Haworth as the potential recruit rather than having the recruit described to her. This has been corrected.